Inscribed quadrilaterals (other)

An inscribed quadrilateral is a four-sided figure whose vertices all lie on a circle. Such quadrilaterals are also called cyclic quadrilaterals. In addition to the basic properties of cyclic quadrilaterals, there are other interesting configurations and results involving inscribed quadrilaterals, such as those with perpendicular diagonals, equal sides, or special angle properties.

Important properties

• If a quadrilateral is inscribed in a circle, the sum of each pair of opposite angles is 180°.

• The perpendicularity of diagonals in an inscribed quadrilateral leads to special relationships among its sides (e.g., Ptolemy's theorem).

• If the diagonals of an inscribed quadrilateral are equal, the quadrilateral is an isosceles trapezium.

• Certain inscribed quadrilaterals have equal sides (e.g., a rectangle or an isosceles trapezium).